The present invention relates to a dichroic mirror having an appropriate half band width.
Heretofore, in a dichroic mirror consisting of alternate layers of high refractive index layers and low refractive index layers, the ratio of optical film thickness in each basic layer for the high refractive index layer and the low refractive index layer has been 1:1 or 3:1.
In a multi-layer film in which the ratio of the film optical thicknesses of high refractive index layers and low refractive index layers is 1:1, a high reflectance can be easily obtained if the ratio of refractive index is high. However, the half band width of the reflective zone becomes excessively large. Also, while an appropriate half band width can be obtained if the ratio of refractive indices is small, the number of layers increases in order to obtain a high reflectance. This makes manufacturing thereof difficult. In a multi-layer film in which the ratio of the optical film thicknesses of high refractive index films and low refractive index films is 3:1, a high ratio of refractive index is required to obtain an appropriate half band width. This is shown in FIG. 1. Here, a curve shows the transmittivity of a ten layer film in which a ratio of optical film thicknesses of high refractive index films with a refractive index of 2.3 and low refractive index films with a refractive index of 1.38 is 1:1. A curve 2 shows the transmittivity of a ten layer film in which the ratio of optical film thicknesses is 3:1 and films have same refractive indexes as those in the curve 1. A curve 3 shows the transmittivity of an eighteen (18) layer film, in which the ratio of optical film thicknesses of high refractive index films with a refractive index of 2.0 and low refractive index films with a refractive index of 1.49 is 1:1. In FIG. 1, the curve 1, represents the characteristics of a mirror in which the ratio of optical film thicknesses of high refractive index films and low refractive index films is 1:1 and the ratio of refractive indices is high. The curve 1 has a large half band width. If one wishes to provide properties with an appropriate half band width such as in the curve 3, the number of layers will become as high as 18. Also when the ratio of optical film thicknesses is 3:1, the half band width becomes small as shown by the curve 2.
The relationship between a combination of refractive indices in an evaporation film and the half band width of the reflective zone is as follows. When a ratio of the wave-number to a reference wave length is represented by g, in a mirror having an optical film thickness ratio 1:1 and a sufficiently large number of layers, one half, .DELTA.g, of the half band width of the mirror film thickness ratio of 1:1 when a number of layers is sufficiently large, is expressed by: ##EQU1## wherein nH is a high refractive index and nL is a low refractive index.
For a film having an optical film thickness ratio of 3:1, the value .DELTA.g is expressed by: ##EQU2##
Relationships between refractive indexes of films of TiO.sub.2 (2.3 to 2.4), ZrO.sub.2 (2.0), SiO.sub.2 (1.49), MgF.sub.2 (1.38) which are frequently used nowadays and their half band widths are shown in Table 1, using both of the above formulae. A reference wave length of a reflective zone is made 440 nm, here.
TABLE 1 ______________________________________ Half band width for a reference wave nH nL length of 440 nm ______________________________________ Ratio of 1:1 2.3 1.38 145 2.0 1.49 83 2.4 1.38 76 Ratio of 3:1 2.3 1.38 71 2.3 1.49 60 ______________________________________
Films with an optical film thickness ratio of 1:1 can have a half band width of 80 nm or above when the ratio of refractive indexes is small such as a high refractive index of 2.0 and a low refractive index of 1.49. However, the number of layers reaches 20 layers or more in order to achieve a high reflectance. Thus, such a film is difficult to manufacture. Also, films having an optical film thickness ratio of 3:1 require films with high refractive indexes of 2.4 or above in order to secure a half band width of 80 nm or above. However a film with high refractive index contains a high dispersion at short wave lengths. Hence its half band width becomes narrow, thus it is difficult to obtain a half band width of 80 nm or above.